This is a strange expression, because “lam” or “lamming” means, according to the free dictionary, to give a thorough beating, thrash, strike, or wallop. “On the lam” has no connection to that definition. The New York Times says the expression means running away or to be a fugitive from the law. One theory is that Allan Pinkerton had explained that pickpockets would utter the word “lam” after lifting a wallet as a signal to get out as soon as possible.